CN103148095B - Full ceramic bearing as well as manufacture method and basic structure parameter determination method thereof - Google Patents

Abstract

The invention relates to a ceramic bearing, and in particular relates to a full ceramic bearing as well as a manufacture method and a basic structure parameter determination method thereof. The basic structure parameter determination method of the full ceramic bearing comprises the following steps of: confirming basic structure parameters of the bearing according to the known structure size of the bearing; selecting the factors and the levels of orthogonal tests, and building an orthogonal test table to determine the test times; carrying out the orthogonal test scheme, and substituting the level of each factor which corresponds to each test into an objective function f(x)i=aCor max+b epsilon min; analyzing the test result, and determining the optimal parameter of each factor; and judging the optimal parameter. According to the basic structure parameter determination method of the full ceramic bearing, the defect caused by the complete coping of the design technology of the existing full steel bearing can be overcome, and the reasonable basic structure parameter of the full ceramic bearing can be obtained; and the practices show that the performance of the full ceramic bearing can be improved and the fatigue life of the full ceramic bearing can be prolonged after the method is used.

Description

The defining method of full-ceramic bearing and manufacture method thereof, elementary structure parameter

Technical field

The present invention relates to ceramic bearing, be related specifically to the defining method of a kind of full-ceramic bearing and manufacture method thereof, elementary structure parameter.

Background technology

Along with the development of technology, more and more higher to the performance requirement of main frame, working condition is also more and more harsher, has higher requirement especially to the bearing used under special operation condition, as high temperature, at a high speed, the working condition such as burn into acid medium.At present, adopt the rolling bearing of high-temperature bearing Steel material, can not work long hours higher than at 250 DEG C of temperature, high temperature lower bearing hardness declines, and the life-span significantly reduces, and the lubrication and cooling system of bearing is quite complicated.Therefore, the high temperature of high-temperature bearing steel making, high-speed bearing, can not reach actual operation requirements.For above situation, traditional high-temperature bearing steel can not meet the demands.Ceramic material can meet above-mentioned harsh working condition requirement, but due to the relevant parameter such as performance parameter, thermal parameter of ceramic material, different from bearing steel material, determine its method for designing different.If the structural parameters indiscriminately imitating existing steel bearings completely design, the performance of ceramic bearing not only can be made to can not get improving, also can design because of mistake, and its performance is significantly reduced, the even premature failure of bearing.

Summary of the invention

The object of the present invention is to provide a kind of defining method of elementary structure parameter of full-ceramic bearing, to obtain the elementary structure parameter of rational full-ceramic bearing.Present invention also offers the manufacture method of the full-ceramic bearing of the defining method of the elementary structure parameter of a kind of full-ceramic bearing and the above-mentioned full-ceramic bearing of use.

To achieve these goals, the defining method of the elementary structure parameter of full-ceramic bearing of the present invention adopts following technical scheme: the defining method of the elementary structure parameter of full-ceramic bearing, comprises the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, the elementary structure parameter of described bearing comprises: inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _w, pitch diameter of ball set Dwp, described constraints is:

A) ball number Z constraints: can operate stable in order to bearing and ensure the intensity of retainer,

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: for improving the bearing capacity of bearing, should increase Ceramic Balls section factor, Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints: for reducing contact stress, improve contact fatigue life, should reduce inner ring Contact stress coefficient fi and outer ring channel Curvature Radius Coefficient fe, its constraints is:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: for improving bearing capacity, should increase contact angle, the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: for making ball group and retainer adapt, ensures bearing flexible rotating, 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f(x) _i=aC _{or max}+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _{or max}represent rated static load, ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ ${\mathrm{\ω}}_{\min }=\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z\left]\right),$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}\mathrm{tg}{\mathrm{\α}}_i-(1+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),$ $\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f(x) _iresult as the test index of each test, the f(x by all tests that i-th level of jth row factor participates in obtain) _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, judgement checking is carried out to optimized parameter,

In formula, d _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding; The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements.

The defining method of the elementary structure parameter of full-ceramic bearing of the present invention, the elementary structure parameter of orthogonal experimental design method to bearing is adopted to be optimized design, by the elementary structure parameter inner ring Contact stress coefficient fi of bearing, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _welect factor as.Ceramic material and the elastic modelling quantity of Steel material and the different of Poisson's ratio, under same load, the relative steel bearings of the contact stress of ceramic bearing increases about 30%, but contact stress increase can reduce the contact fatigue life of bearing; The crushing load of Ceramic Balls is higher than steel ball, and the density of Ceramic Balls is little, and centrifugal force is little.According to the above-mentioned performance parameter of ceramic material, determining the constraints of bearing elementary structure parameter, by reducing inner ring Contact stress coefficient and outer ring channel Curvature Radius Coefficient, reducing contact stress, and by relatively increasing sphere diameter and contact angle, improve the bearing capacity of bearing.Then, according to the constraints of bearing elementary structure parameter, determine the level of each factor, set up orthogonal test table, determine the scheme of orthogonal experiment scheme according to this orthogonal test.In order on the basis of pursuing minimum contact stress, reduce spin to roll ratio simultaneously, the present invention adopts method of weighting scores, set up a multiobject majorized function (rated static load, spin to roll ratio), calculate the object function of each test, by the test of less number of times, just can comprehensively analyze each factor and optimize, and then the optimized parameter of each factor can be found fast, then optimized parameter is verified, until optimized parameter meets the requirements, this optimized parameter is the elementary structure parameter of full-ceramic bearing.The method overcome the deficiency of the designing technique indiscriminately imitating existing all-steel bearing.Under 250 DEG C of high temperature, at a high speed 20000 revs/min, complete the all-steel bearing B7208 life test of 50 hours, and press the full-ceramic bearing of the determination method design of above-mentioned elementary structure parameter, model is identical with all-steel bearing, complete 150 hours life tests at identical conditions, in process of the test, the test temperature of full-ceramic bearing, lower than the test temperature of all-steel bearing, is more conducive to bearing operation performance and life-span.Certainly, because ceramic material has anticorrosive, acid medium, meet bearing performance and the life requirements of full-ceramic bearing.Therefore, the parameter value of the full-ceramic bearing elementary structure parameter adopting the present invention to obtain is more reasonable, be proven, not only increase performance and the fatigue life of full-ceramic bearing by the full-ceramic bearing of the determination method design of above-mentioned elementary structure parameter, also enable full-ceramic bearing meet the instructions for use of special operation condition (high temperature, at a high speed, burn into acid medium).

To achieve these goals, the manufacture method of full-ceramic bearing of the present invention adopts following technical scheme: comprise the following steps:

1) determine the elementary structure parameter of full-ceramic bearing, comprise the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, the elementary structure parameter of described bearing comprises: inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _w, pitch diameter of ball set Dwp, described constraints is:

A) ball number Z constraints: can operate stable in order to bearing and ensure the intensity of retainer,

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: for improving the bearing capacity of bearing, should increase Ceramic Balls section factor, Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints: for reducing contact stress, improve contact fatigue life, should reduce inner ring Contact stress coefficient fi and outer ring channel Curvature Radius Coefficient fe, its constraints is:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: for improving bearing capacity, should increase contact angle, the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: for making ball group and retainer adapt, ensures bearing flexible rotating, 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f(x) _i=aC _{or max}+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _{or max}represent rated static load, ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ ${\mathrm{\ω}}_{\min }=\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z\left]\right),$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}\mathrm{tg}{\mathrm{\α}}_i-(1+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),$ $\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f(x) _iresult as the test index of each test, the f(x by all tests that i-th level of jth row factor participates in obtain) _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, judgement checking is carried out to optimized parameter,

In formula, d _c---retainer internal diameter; Z---ball number, S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements.

2) according to the elementary structure parameter of above-mentioned full-ceramic bearing and the known structure size of bearing: the internal diameter d of bearing, outer diameter D, draw out the drawing of bearing, and process full-ceramic bearing according to described drawing.

To achieve these goals, full-ceramic bearing of the present invention adopts following technical scheme: full-ceramic bearing, comprise outer ring, inner ring, Ceramic Balls and retainer, bearing elementary structure parameter comprises inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z, sphere diameter D _wwith pitch diameter of ball set Dwp, described outer ring, inner ring, Ceramic Balls and retainer all adopt ceramic material to make, the parameter value that the defining method that described bearing elementary structure parameter has the elementary structure parameter adopting full-ceramic bearing obtains, the defining method of the elementary structure parameter of described full-ceramic bearing comprises the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, described constraints is:

A) ball number Z constraints: can operate stable in order to bearing and ensure the intensity of retainer,

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: for improving the bearing capacity of bearing, should increase Ceramic Balls section factor, Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints: for reducing contact stress, improve contact fatigue life, should reduce inner ring Contact stress coefficient fi and outer ring channel Curvature Radius Coefficient fe, its constraints is:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: for improving bearing capacity, should increase contact angle, the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: for making ball group and retainer adapt, ensures bearing flexible rotating, 0.5 (D+d)≤Dwp≤0.505 (D+d),

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f(x) _i=aC _{or max}+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _{or max}represent rated static load, ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ ${\mathrm{\ω}}_{\min }=\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z\left]\right),$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}\mathrm{tg}{\mathrm{\α}}_i-(1+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),$ $\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f(x) _iresult as the test index of each test, the f(x by all tests that i-th level of jth row factor participates in obtain) _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, judgement checking is carried out to optimized parameter,

D _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements..

Accompanying drawing explanation

Fig. 1 is the structural representation of full-ceramic bearing.

Detailed description of the invention

A kind of embodiment of the defining method of the elementary structure parameter of full-ceramic bearing of the present invention, comprises the steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, the elementary structure parameter of described bearing comprises: inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _w, pitch diameter of ball set Dwp, described constraints is:

A) ball number Z constraints: can operate stable in order to bearing and ensure the intensity of retainer,

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: the section factor 0.28 ~ 0.32 of steel ball, the crushing load of Ceramic Balls is higher than steel ball, the density of Ceramic Balls is little, centrifugal force is little, the bearing capacity of bearing during for running up, compared with steel ball size, Ceramic Balls section factor should get higher value, Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints: for reducing contact stress, improve contact fatigue life, should reduce inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, its constraints is:

0.505≤fi≤0.515，0.510≤fe≤0.520

D) pitch diameter of ball set Dwp constraints: for making ball group and retainer adapt, ensures bearing flexible rotating, 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

E) contact angle α: contact angle is larger, and axial carrying capacity is larger, and when running up, spin to roll ratio is larger, generates heat more serious; Material property parameter due to ceramic bearing is beneficial to and runs up, and the heat that ceramic bearing produces is less than steel bearings, and for improving the bearing capacity of ceramic bearing, should relatively increase its contact angle, the span of contact angle is 20 ° ~ 45 °.

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m.In the present embodiment, the initial value of the pitch diameter of ball set preset is Dwp=0.5(D+d), four levels of inner ring Contact stress coefficient fi get 0.505,0.508,0.510,0.515 respectively; Four levels of outer ring channel Curvature Radius Coefficient fe get 0.510,0.512,0.515,0.520 respectively; Preset a reference value alpha ₀, α contact angle four levels get α respectively ₀-2 °, α ₀, α ₀+ 2 °, α ₀+ 4 °; Sphere diameter D _wfour levels accurate sphere diameter value Dw1 of label taking respectively, Dw2, Dw3, Dw4; Ball number Z gets Z respectively according to four levels of fe ₀-3, Z ₀-2, Z ₀-1, Z ₀; Orthogonal test table has selected L ₁₆(4 ⁵) orthogonal arrage, as shown in table 1, test number (TN) is 16 times.

Table 1 orthogonal test scheme table

In above-mentioned table 1, f(x) _irepresent the test index tested for i-th time, represent the result of the test of the i level of jth row, computing formula as follows:

$K_1^{\left(1\right)}=f_1+f_2+f_3+f_4,$

$K_2^{\left(1\right)}=f_5+f_6+f_7+f_8,$

$K_3^{\left(1\right)}=f_9+f_{10}+f_{11}+f_{12},$

$K_4^{\left(1\right)}=f_{13}+f_{14}+f_{15}+f_{16},$

$K_1^{\left(2\right)}=f_1+f_5+f_9+f_{13},$

$K_2^{\left(2\right)}=f_2+f_6+f_{10}+f_{14},$

$K_3^{\left(2\right)}=f_3+f_7+f_{11}+f_{15},$

$K_4^{\left(2\right)}=f_4+f_8+f_{12}+f_{16},$

$K_1^{\left(3\right)}=f_1+f_6+f_{11}+f_{16},$

$K_2^{\left(3\right)}=f_2+f_5+f_{12}+f_{15},$

$K_3^{\left(3\right)}=f_3+f_8+f_9+f_{14},$

$K_4^{\left(3\right)}=f_4+f_7+f_{10}+f_{13},$

$K_1^{\left(4\right)}=f_1+f_7+f_{12}+f_{14},$

$K_2^{\left(4\right)}=f_2+f_8+f_{11}+f_{13},$

$K_3^{\left(4\right)}=f_3+f_5+f_{10}+f_{16},$

$K_4^{\left(4\right)}=f_4+f_6+f_9+f_{15},$

$K_1^{\left(5\right)}=f_1+f_8+f_{10}+f_{15},$

$K_2^{\left(5\right)}=f_2+f_7+f_9+f_{16},$

$K_3^{\left(5\right)}=f_3+f_6+f_{12}+f_{13},$

$K_4^{\left(5\right)}=f_4+f_5+f_{11}+f_{14},$

mean value be wherein j=1,2 ... 5, i=1,2,3,4, namely in the present embodiment, 5 factors are to there being 5 row, and each row is to there being 4 levels.

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f(x) _i=aC _{or max}+ b ε _min, i=1,2---m, in the present embodiment, m=16, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _{or max}represent rated static load, ε _minrepresent spin to roll ratio, the meaning of this object function is on the basis of pursuing minimum contact stress, reduces spin to roll ratio simultaneously, is namely ensureing, under the prerequisite improving rated static load, to reduce spin to roll ratio simultaneously. $C_{\mathrm{or}}=f_0\×i\×Z\×D_W^2\×\cos \mathrm{\α},$ ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ ${\mathrm{\ω}}_{\min }=\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z\left]\right),$ ω _minrepresent and make the maximum spin to roll ratio minimization of Ceramic Balls, $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}\mathrm{tg}{\mathrm{\α}}_i-(1+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),$ $\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{\mathrm{Dw}\cos {\mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f(x) _iresult as the test index of each test, the f(x by all tests that i-th level of jth row factor participates in obtain) _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, judgement checking is carried out to optimized parameter,

In formula, d _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements.

In other embodiment of the defining method of the elementary structure parameter of full-ceramic bearing of the present invention, the number of levels that each factor is selected can also be 2 or 3 or 5 or 6, and the number of levels of each factor can be equal, also can be unequal.

In other embodiment of the defining method of the elementary structure parameter of full-ceramic bearing of the present invention, under pitch diameter of ball set constraints 0.5 (D+d)≤Dwp≤0.505 (D+d), the initial value of pitch diameter of ball set can also be got and be not equal to 0.5(D+d) arbitrary value.

As for a kind of full-ceramic bearing, the parameter of this angular contact ball bearing known comprises: internal diameter is 40mm, and external diameter is 80mm, and width is 18mm, and its working speed is 42000 revs/min.The outer ring of this bearing, inner ring, Ceramic Balls and retainer material all adopt silicon nitride ceramics.The defining method of the elementary structure parameter of the full-ceramic bearing of the invention described above is used to determine that the concrete steps of the elementary structure parameter of this full-ceramic bearing are:

1, the initial value getting pitch diameter of ball set is Dwp=0.5(D+d)=60, four levels of inner ring Contact stress coefficient fi get 0.505,0.508,0.510,0.515 respectively; Four levels of outer ring channel Curvature Radius Coefficient fe get 0.510,0.512,0.515,0.520 respectively; Preset a reference value alpha ₀=22 °, four levels of α contact angle get 20 °, 22 °, 24 °, 26 ° respectively; Sphere diameter D _wfour levels accurate sphere diameter values 11.906,12,12.303,12.5 of label taking respectively; Ball number Z gets 9,10,11,12 respectively according to four levels of fe; Orthogonal test table has selected L ₁₆(4 ⁵) orthogonal arrage, as shown in table 2, test number (TN) is 16 times.

Table 2 orthogonal test scheme table

2, according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f(x) _i=aC _{or max}+ b ε _min, i=1,2---m, in the present embodiment, m=16, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _{or max}represent rated static load, ε _minrepresent spin to roll ratio, the meaning of this object function is on the basis of pursuing minimum contact stress, reduces spin to roll ratio simultaneously, is namely ensureing, under the prerequisite improving rated static load, to reduce spin to roll ratio simultaneously. $C_{\mathrm{or}}=f_0\×i\×Z\×D_W^2\×\cos \mathrm{\α},$ ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ ${\mathrm{\ω}}_{\min }=\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z\left]\right),$ ω _minrepresent and make the maximum spin to roll ratio minimization of Ceramic Balls.

3, test index f(x is utilized) _iresult of calculation, use mean value be wherein j=1,2 ... 5, i=1,2,3,4, determine 5 factors, the optimum level of each factor.Obtained the optimum level of each factor of full-ceramic bearing by computational analysis: outer ring channel Curvature Radius Coefficient fe's is 0.515, inner ring Contact stress coefficient fi is 0.505; Contact angle α is 20 °, Ceramic Balls sphere diameter D _wfor 12.303mm, ball number Z is 11.

4, then according to following condition, judgement retainer intensity is carried out to optimized parameter, S _b> 1, the sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter.

The embodiment of the manufacture method of full-ceramic bearing of the present invention, comprises the following steps: the elementary structure parameter 1) determining full-ceramic bearing; 2) according to elementary structure parameter and the known structure size (the internal diameter d of bearing, outer diameter D) of above-mentioned full-ceramic bearing, draw out the drawing of full-ceramic bearing, and process full-ceramic bearing according to described drawing.Identical with the step of the defining method of the elementary structure parameter of above-mentioned full-ceramic bearing in the step 1) of this enforcement, at this no longer repeated description.

The embodiment of full-ceramic bearing of the present invention, as shown in Figure 1: full-ceramic bearing comprises outer ring, inner ring, Ceramic Balls and retainer, described outer ring, inner ring, Ceramic Balls and retainer all adopt ceramic material to make, and bearing elementary structure parameter comprises inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z, sphere diameter D _wwith pitch diameter of ball set Dwp, inner ring Contact stress=D _wfi, outer ring channel radius of curvature=D _wfe, the parameter value that the defining method that described bearing elementary structure parameter has the elementary structure parameter adopting full-ceramic bearing obtains.The defining method of the elementary structure parameter of described full-ceramic bearing is identical with the step of the defining method of the elementary structure parameter of the full-ceramic bearing of the invention described above, at this no longer repeated description.

Claims (3)

1. the defining method of the elementary structure parameter of full-ceramic bearing, is characterized in that, comprises the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, the elementary structure parameter of described bearing comprises: inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _w, pitch diameter of ball set Dwp, described constraints is:

A) ball number Z constraints:

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f (x) _i=aC _ormax+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _ormaxrepresent rated static load, $C_{\mathrm{or}}=f_0\×i\×Z\×D_W^2\×\cos \mathrm{\α},$ ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ $\mathrm{\ω}\min =\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z)],$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}{\mathrm{tg\α}}_i-(1+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f (x) _iresult as the test index of each test, by the f (x) that all tests that i-th level of jth row factor participates in obtain _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, optimized parameter is verified,

In formula, d _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements.

2. the manufacture method of full-ceramic bearing, is characterized in that: comprise the following steps:

1) determine the elementary structure parameter of full-ceramic bearing, comprise the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, the elementary structure parameter of described bearing comprises: inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D _w, pitch diameter of ball set Dwp, described constraints is:

A) ball number Z constraints:

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f (x) _i=aC _ormax+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _ormaxrepresent rated static load, $C_{\mathrm{or}}=f_0\×i\×Z\×D_W^2\×\cos \mathrm{\α},$ ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ $\mathrm{\ω}\min =\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z)],$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}{\mathrm{tg\α}}_i-(1+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f (x) _iresult as the test index of each test, by the f (x) that all tests that i-th level of jth row factor participates in obtain _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, optimized parameter is verified,

In formula, d _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements;

2) according to the elementary structure parameter of above-mentioned full-ceramic bearing and the known structure size of bearing: the internal diameter d of bearing, outer diameter D, draw out the drawing of bearing, and process full-ceramic bearing according to described drawing.

3. full-ceramic bearing, comprises outer ring, inner ring, Ceramic Balls and retainer, and bearing elementary structure parameter comprises inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z, sphere diameter D _wwith pitch diameter of ball set Dwp, it is characterized in that: described outer ring, inner ring, Ceramic Balls and retainer all adopt ceramic material to make, the parameter value that the defining method that described bearing elementary structure parameter has the elementary structure parameter adopting full-ceramic bearing obtains, the defining method of the elementary structure parameter of described full-ceramic bearing comprises the following steps:

A. according to the known structure size of bearing: the internal diameter d of bearing, outer diameter D, to the elementary structure parameter setting constraints of bearing, described constraints is:

A) ball number Z constraints:

$Z\≤\frac{\mathrm{\π}\·\mathrm{Dwp}}{(1.01+1.9/D_W)D_W}$

In formula: Dwp---pitch diameter of ball set; Z---ball number; D _w---sphere diameter;

B) sphere diameter D _wconstraints: Ceramic Balls section factor is 0.28 ~ 0.34, that is:

0.28(D-d)≤D _W≤0.34(D-d)

In formula: D, d---the external diameter of bearing and internal diameter;

C) raceway groove constraints:

0.505≤fi≤0.515，0.510≤fe≤0.520

E) contact angle α: the span of contact angle is 20 ° ~ 45 °;

D) pitch diameter of ball set Dwp constraints: 0.5 (D+d)≤Dwp≤0.505 (D+d)

In formula: Dwp---pitch diameter of ball set;

B. inner ring Contact stress coefficient fi, outer ring channel Curvature Radius Coefficient fe, contact angle α, ball number Z and sphere diameter D is chosen _was 5 factors of orthogonal test, an initial value of pitch diameter of ball set Dwp is set according to the constraints d in above-mentioned steps A, then the level of each factor described is chosen according to other constraints in above-mentioned steps A, the number of levels of each factor is at least two, orthogonal test table is set up according to above-mentioned factor and level, each factor in this orthogonal test table is arranged in column direction, each level is arranged by line direction, determines that test number (TN) is m;

C. implement orthogonal test scheme: according to above-mentioned orthogonal test table, the level at every turn testing each corresponding factor is substituted into object function f (x) _i=aC _ormax+ b ε _min, wherein, i=1,2---m, a, b are weight coefficient, and b=1-a, a get 0.5 ~ 0.7, b and get 0.3 ~ 0.5, C _ormaxrepresent rated static load, $C_{\mathrm{or}}=f_0\×i\×Z\×D_W^2\×\cos \mathrm{\α},$ ε _minrepresent spin to roll ratio, ${\mathrm{\ϵ}}_{\min }=\frac{{\mathrm{\ω}}_{\mathrm{be}}^s}{{\mathrm{\ω}}_{\mathrm{be}}^r}=\frac{1}{{\mathrm{\ω}}_{\min }},$ $\mathrm{\ω}\min =\min \left(\max \right[{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_1,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_2,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_3,...,{\left(\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}\right)}_Z)],$ $\frac{{\mathrm{\ω}}_s}{{\mathrm{\ω}}_R}=\frac{\mathrm{Dw}\cos {\mathrm{\α}}_i}{\mathrm{Dwp}}{\mathrm{tg\α}}_i-(1+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_i}{\mathrm{Dwp}})\mathrm{tg}({\mathrm{\α}}_i-\mathrm{\β}),\mathrm{tg}\left(\mathrm{\β}\right)=\frac{\cos {\mathrm{\α}}_e\sin {\mathrm{\α}}_e}{{\cos }^2{\mathrm{\α}}_e+\frac{{\mathrm{Dw}\cos \mathrm{\α}}_e}{\mathrm{Dwp}}},$ F ₀for rated static load coefficient, represent inner ring spin to roll ratio, ω _sfor Ceramic Balls roll rate, ω _rrepresent Ceramic Balls rolling speed, α _iceramic Balls and inner ring contact angle, α _eceramic Balls and outer ring contact angle, D _wfor sphere diameter, Dwp is pitch diameter of ball set, and β is that outer raceway controls attitude angle; By above-mentioned f (x) _iresult as the test index of each test, by the f (x) that all tests that i-th level of jth row factor participates in obtain _ibe added and obtain as the result of the test of i-th level of jth row factor;

D. the result of the test corresponding to all levels in each row factor is analyzed respectively maximum with numerical value corresponding level, as the optimized parameter of jth row factor, finally determines the optimized parameter of 5 factors;

E. then according to following condition, optimized parameter is verified,

In formula, d _c---retainer internal diameter; Z---ball number; S _b---cross deck-siding;

The sphere diameter D chosen _wwith number Z meets minimum lintel value requirement between retainer pocket hole, namely this optimized parameter is defined as bearing elementary structure parameter, does not meet the demands, and then gets back to step B, until optimized parameter meets the requirements.